Given a random initial condition \(Z_{0}\)  drawn from
\(\mathcal {N}(\mathbf {0},\mathbf {I}_{n})\) ,
we generate a sequence of “true” hidden states \((z^*_k)_k\) 
and a sequence of synthetic observations
\((y_k^*)_k\)  with the same model used for filtering. We are thus in the usual “identical twin experiment” setting [1]},
wherein
the filtering algorithms must
estimate the true state
given only these synthetic observations.
